Ok, so the tube steps come off and leave factory sliders. This is great news, I had no clue. Over the summer I went up mineral basin in my T, no lift on 35" tires. The sliders and UCP got a work out. I haven't crawled under the H2 to really check it out yet (crappy winter weather here and my 2 lives in the driveway), but it seems the H2 stuff is better tucked up and protected. Plus the H2 wheelbase is about a foot shorter and the H2 sits a bit higher. I can accept that factory sliders are sufficient for most UT trails. If I bend a stock slider, I'll replace it with a Rocky-Road.
An update? At this point I'd say you are correct on all counts. The 2 is big and comfortable, and needs 37" tires for looks if nothing else. I suspect you are also correct on the suspension/steering parts that need replacing, although Murdock Chevy gave me the run-around and decided it just needed adjustment when I asked them to pay during the 5 day "no questions asked" return period. I'll let Jerry Seiner have a look when it's time for my next oil change. One other thing you were right about, the interior rattles a bit on rough roads. Nothing as bad as the windshield rattle, more of a subtle creaking, but all in all my H3 and H3T just felt and sounded a bit more solid.
I think it will work out well for me, but until I get it out on some trails and do some wheeling I remain unconvinced that it's better off-road than an H3 Alpha w/off-road package. Either way, if one is slightly better than the other it's not going to matter. I can still get out and wheel it, get to all my camping spots, and the H2 has a lot more room for people, gear, and my dogs. To put it another way, I bought the H2 only because I gave up on finding an H3 Alpha/off-road for a reasonable price within 100 miles. If I had to do it over and could choose between an H2 and the kind of H3 Alpha I was searching for I'm not sure which one I'd pick. It's rapidly growing on me.
Back to the Mineral Basin run I was talking about... Here is a video I found on youtube of the trail. No clue who they are, and I ran it much later in the season when it was dry, but it shows roughly the first half or 2/3 of the trail. Skip to around 3:20 to see the part of the trail called the rock garden. It should be clear why my sliders and UCP got a work-out on my T. I'd be surprised of twin never ran this trail, it's fairly popular...
https://www.youtube.com/watch?v=f4IjbA_3vxU
edit: I really didn't enjoy the rock garden area. Tons of big loose rocks, getting thrown around, lots of potential damage... That was my second time running it, the first time was years ago in a Cherokee with about 5.5" of lift and 32" tires and snow blocked the trail just past the rock garden. I think the second time will be my last. It's just not a fun trail to me.